Download Exponent Review

Exponent Review
Product Rule
If m and n are positive integers and a is a real number, then am ∙ an = am + n.
Quotient Rule
am
If m and n are positive integers and a is a real number, then n  a mn , a ≠ 0.
a
Examples: Use the product rule to simplify.
a. y3 ∙ y
b. (2x2)(-3x5)
 35
2x 5 y 2
e.
f.
xy
 32
White Board Activity:
Practice: Use the product rule to simplify.
a. r5 ∙ r
b. (6x3)(-2x9)
 214
7x 4 y11
e.
f.
xy
 210
c. (x2y)(x3y2)
d. (-a7a4)(3ab9)
c. (m5n10)(mn8)
d. (-x9y)(4x2y11)
Power Rule for Exponents
If m and n are positive integers and a is a real number, then (am)n = amn.
Examples: use the power rule to simplify each expression.
a. (53)6
b. (y8)2
White Board Activity:
Practice: Use the power rule to simplify each expression.
a. (94)10
b. (z6)3
Power of a Product Rule
If n is a positive integer and a and b are real numbers, then (ab)n = anbn.
Power of a Quotient Rule
n
an
a
If n is a positive integer and a and b are real numbers, then    n , c ≠ 0.
b
b
Examples: Simplify each expression.
a. (2a)
3
2 3
2
b. (-5x y z)
3 5
c. (-xy )
 2x 4
d.  5
 3y



4
White Board Activity:
Practice: Simplify each expression.
4
4 2 3
a. (3y)
b. (-2p q r)
4
 5x 6
d.  3
 9y
7
c. (-a b)
Zero Exponent Rule
a0 = 1, as long as a is not 0.
Examples: Simplify each expression.
a. (5x3y2)0
b. (-4x)0
c. -4x0
White Board Activity
Practice: Simplify each expression.
a. (2r2s)0
b. (7y)0
c. 7y0
Using the rules together.
Examples: Simplify each expression.
a. (9y5)2
 3y 7
b.  5
 6x



2
White Board Activity
Practice: Simplify each expression.
4 4
a. (3y )
 7x 9
b. 
6
 14y



2a b 
3
c.
2
c.
4 3
 8a 9 b 2
3a
2

3
b 45
 27a 6 b 4
Negative Exponent Rule
If a is a real number other than 0 and n is an integer, then a-n =
1
1
and -n = an.
n
a
a
Examples: Simplify by writing each expression with positive exponents only.
a. 5-3
b. (-3)-4
c. 7x-4
6
d.  
y
2
e.
y 9
z 5
f.
y 4
z6
White Board Activity
Practice: Simplify by writing each expression with positive exponents only.
a. 3-2
b. (-2)-4
c. 2x-3
2
d.  
x
3
e.
p 4
q 9
f.
x 5
y7



2
Using the rules together.
Examples: Simplify each expression. Write each result using positive exponents only.
 
x 2x 3
a.
x7
4
 3a 2
b. 
 y



2
c. (y-3b6)-6
3a 4 b 0 c 6
f.
6ab 2 c 8
3 -2
e. (5y )
22a 7 b 5
g. 
11a 2 b 3
d.
h.
x 7
x 
4 3
2xy 3
x y 
3 2
2
White Board Activity
Practice: Simplify each expression. Write each result using positive exponents only.
 
x 3x 5
a.
x4
2 -3
e. (4a )
3
 9x 3
b. 
 y



2
5x 7 y 3 z 0
f.
15xy 8 z 3
c. (a-4b7)-5
32x 3 y 6
g. 
8x 5 y  2
d.
y 10
y 
4 5
3x y 
2x y 
2
h.
7
2
3